On the other hand, interest for the effect of spatial inhomogeneity on the vacuum pair production is triggered by the advances in theoretical works and the numerical computation techniques [1]}, [2]}, [3]}, [4]}, [5]}. These works have provided new features of finite spatial field pair production, such as self-bunching effect [1]}, ponderomotive force [2]}, spin field interaction [5]} and so on. Recently, Kohlfürst has studied vacuum pair production in strong electromagnetic field, by considering both of electric and magnetic field with spatial inhomogeneity and has revealed the competitive results between the multiphoton and tunneling process [9]}, [5]}. All these findings emphasize the importance of considering spatial variations for vacuum pair production in the strong external field.
